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Simplifying 0.75(24 + -20t) + 9t = 2(5t + 1) (24 * 0.75 + -20t * 0.75) + 9t = 2(5t + 1) (18 + -15t) + 9t = 2(5t + 1) Combine like terms: -15t + 9t = -6t 18 + -6t = 2(5t + 1) Reorder the terms: 18 + -6t = 2(1 + 5t) 18 + -6t = (1 * 2 + 5t * 2) 18 + -6t = (2 + 10t) Solving 18 + -6t = 2 + 10t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10t' to each side of the equation. 18 + -6t + -10t = 2 + 10t + -10t Combine like terms: -6t + -10t = -16t 18 + -16t = 2 + 10t + -10t Combine like terms: 10t + -10t = 0 18 + -16t = 2 + 0 18 + -16t = 2 Add '-18' to each side of the equation. 18 + -18 + -16t = 2 + -18 Combine like terms: 18 + -18 = 0 0 + -16t = 2 + -18 -16t = 2 + -18 Combine like terms: 2 + -18 = -16 -16t = -16 Divide each side by '-16'. t = 1 Simplifying t = 1
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